Yeah, for this problem, we are given the total power of the engine. So total power is 28 kilowatt. Let's convert this kilowatt as the unit of what? And we know that one kilowatt is 1000 what? So 28 kg what? One kilowatt is equivalent to 1000 what? Sir, kilowatt and kilowatt will cancel. And then we will lift up with 20,000 what? And w is the unique for what? And then the constant velocity of the truck is given us 60 kilometer or our again kilometer per hour have to be expressed in metric unit. So for metric unit, one kilometer is 1000 m and then one hour is 60 minutes. And we know that in one minute we have 60 seconds. So 60 times 60 is 3600 2nd. Alright, So 60 kilometer par our All right. And then one hour half, 3600 2nd, and then one kilometer is equivalent to 1000 m. So kilometer and kilometer will cancel. Our and our will cancel. We will left of it meet up our second. So 60 times 1000 divided by 3600 years equivalent to Uh huh. 16.67 m/s. All I'm doing is is writing down what is provided on the problem and then expressing a in metric unit. All right. And then we are given the force due to air friction is directly proportional to square of the velocity. So what is given an equation is force due to here friction. Let it be denoted as F forced you to a friction is directly proportional to the square of the velocity of these develop city. And we all know that proposal sign is always replaced with a proportional consent for the scarce. Let it be denoted by. Okay, Okay. Now, if A is equivalent to k B square. All right. Now, the first part of the problem is we have to find the power of the engine. All right, So, what is the power of the engine? So, power is defined as the force times. Speak. Okay, now, over here, we don't know what is the total resistive force. Okay, we know speed. We are given power. So let's figure out what is the force. Actually? This is the resistive force. All right, Power is 28,000. We don't know what is the resistive force of the truck. Right? And then we just calculate speed as 16.67. All right now, we have to find resistive force and get rid of 16.671 method is dividing both sides of the equation by 16.67 so that our right hand side will left await resistive force. Okay? So, if you do matter over here, this too will be canceled. All right. This will give us resistive force is equivalent to 28,000 divided by 16.67 is equivalent to 168 year old newton. So, this is the first part of the problem. All right. Now, for a second part, What we are keeping is now 65% is of the resistive forces due to rolling friction. Okay, so now here's a step force due to rolling friction Is equivalent to 65% off resistive force. So 65% infraction is 65 over 100 with us 0.65 And our resistive force is 1680 Which we calculate on first part. Right? So the resistive force to to rolling friction happened to be. If you do this matt, then that would be equivalent to 109 to newton. Okay, So resistive force to to ruling friction. All right, this is another part. All right. So, and it says the rest is because of air friction. So out of 100%, is rolling friction. Right then, 65, -65 will be 35%. So, that means 35 percent off registered force is due to air friction. So, that means due to air friction will be 35% off 168 year olds. A 35% is 0.35. Alright. 1 680. And if we do mats over here, then that will be equivalent to 587.99 The unit of forces Newton. All right. So that will be equivalent to 587.99 Newton. So, this is the legislative forced to to air friction and then due to rolling friction is €1.9 to newton. Let's recall the equation that is given as if he is key The square we know velocity. Now we got the value of resisting forced into a friction. Then by plugging on this value on this equation, then we can calculate the value of kids. So if a is 587.99 K. Is the proportional constant. Our velocity was 60 kilometers per hour, which is 16.66 m per second. All right now, let's solve for K. K. Is dividing both sides by 16.67 587.99 divided by 16.67 whole square. And if we do match over here, this will give us the value of K. S 2.116 And it's a constant. Right? So, okay, is it devaluing too? 2.116. Okay, the second part of the problem, we have to find the power of the truck if the velocity is 30 km/h. So initial, initially the velocity was 60 km/h right now, at speed 30 kilometer per hour. What is the power of the truck? That's what we have to figure out now for 30 kilometer per hour. Right. That is 30 kilometer per hour hour. Now, you must be comfortable to convert kilometer to meet her by multiplying by 1000 and then convert one over our as 36 years zero second. And if we do match at 30 kilometers per hour, will be equivalent to 8.33 major per second. Now, let's see what is the power At 8.33 m/s, velocity. And power is force times speed. Right? So let's find out what is the total resistive force. Okay, let's recall the idea. Total resistive force is register forced you to rolling friction, which is not going to chance. But the register forced due to air friction depends on K and V. Square. When velocity chance then the value will chance. All right, let's figure out what is it? 1092 The value of key with this constant one chance 2.116. Our new velocity is 8.33 whole square. Okay, and when we do this mad then total resistive force will be equivalent to 123, 8-7. Newton. Okay, we got force and we know the velocity. Now let's find out what is the power. So therefore power is force times speed. Now our new forces 1238.8 to 7 newton. And then our new speed is 8.33 So if we do maths over here we will be give Alan too. If you multiply these 21 Do you know three? 19.4 to what? But we have to express the unit of power in kilowatts. So in at the first step we convert from kilowatt to what? By multiplying multiplying by 1000. Now we have to convert from water kilowatts. So this reverse. So to convert from one particular what we have to divide by 1000. Okay, so the power of the engine, if you divide this then that will be 10.319 You can just round it up as 10.32 kg. What? Also we are X. To express the power in horsepower. The Conversing Unit is one. Horse. Power is 746. What? Okay, so again Power is 10319.42 Okay, divided by 746 hearse. Power. Okay? And if you divide 12319 .42 divided by 746, then we will lift up with 13.8 hers power. So the power of the engine in terms of hers power is 13.8. Okay, so the last part of the problem is we did for 60 kilometers per hour. We did for 30 kilometer per hour. Now we have defined for vehicles 1 20 kilometer for our what is the power in terms of speed? 1 20 kilometer part our So let's convert it into meter or 2nd. So this is a gravelly in two 33.33 m per second. Our new speed is 33.33 m per second. Now let's follow the similar procedure and same state state. So total resistive force. Yes resistive force due to ruling friction which is not going to chance. And then the resistive force due to air friction is KV square. Since we have new velocity right? Our key is 2.116 And then our new velocity is 33 point 33 square. And if we do this map the in total resistive force will be covalin 23442.9. Newton. Now power is fourth times speed. Our new power is 3442.9. And then our new speed is 33.33 If you do maths of the hill, that will give us 114751 What? Right again, we have to convert it into kilowatt. So divided by 1000 right 751 divided by 1000 in kilowatts. Soapy is equivalent to 11 four point 75 kill, oh, what, and then another two expressed it in horsepower, right, He is equivalent to 114751 over, divide by 746. Then that will give us the power is equivalent to 154 horse power. So these are the power in terms of 60 km/h for the first part, And then for second part, we have velocity 30 km/h, and then for velocity 120 km/h in terms of kilowatt and hearst power.