A truck on a straight road starts from rest, accelerating at 2ms-2 , until it reaches a speed of 20ms-1 . Then the truck travels at a constant speed for 20s until the brakes are applied causing the truck to decelerate uniformly to stop it in additional 5s .(a) For how much time the truck is in motion?(b) What is the average speed of the truck for its entire motion?

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meakQueueksiu7e · Accepted Answer

Step 1: Given DataA truck is accelerating while traveling on a straight road a=2ms-2the truck&#039;s initial velocity, u=0ms-1The final velocity of the truck, v=20ms-1The truck travels at a constant speed for a time, t2=20sThe time required to stop after brakes are applied, t3=5sStep 2: Determine the total time for which the truck is in motionLet the time it takes to attain  20ms-1  as the final velocity be t1 .As we know that the first equation of motion is v=u+at⇒t1=v-ua⇒t1=20-02⇒t1=10sThus, the total time for which the truck is in motion is t=t1+t2+t3=10+20+5=35sStep 3: Determine the distance covered by the truck for the first 10sAs we know that the second equation of motion is S=ut+12at2Let the distance traveled for the first 10s be S1⇒S1=0+12×2×102⇒S1=100mStep 4: Determine the distance covered by the truck for the next 20sFor next 20s the truck moved at a constant speed. Hence, a=0ms-1Let the distance traveled for the next 20s be S2On applying the given data in S=ut+12at2 we get,⇒S2=20×20+0⇒S2=400mStep 5: Determine the distance covered by the truck for the last 5sFor the last 5s the truck gets stopped after applying brakesLet the distance traveled for the last  5s be S3On applying the equation, S=12(v+u)t⇒S3=1220+0×5⇒S3=50mThus, the total distance covered by the truck is S=S1+S2+S3=100+400+50=550mStep 6: Determine the average speed of the truckAveragespeed=TotaldistanceTotaltimetaken                         =St=55035=15.7ms-1Final Answer:  (a) The total time for which the truck is in motion is 35s.(b) The average speed of the truck for its entire motion is 15.7ms-1.

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