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?

inframundosa921

inframundosa921

Answered question

2023-03-25

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?

Answer & Explanation

meakQueueksiu7e

meakQueueksiu7e

Beginner2023-03-26Added 5 answers

Step 1: Given Data
A truck is accelerating while traveling on a straight road a=2ms-2
the truck's initial velocity, u=0ms-1
The final velocity of the truck, v=20ms-1
The truck travels at a constant speed for a time, t2=20s
The time required to stop after brakes are applied, t3=5s
Step 2: Determine the total time for which the truck is in motion
Let 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=10s
Thus, the total time for which the truck is in motion is t=t1+t2+t3=10+20+5=35s
Step 3: Determine the distance covered by the truck for the first 10s
As we know that the second equation of motion is S=ut+12at2
Let the distance traveled for the first 10s be S1
S1=0+12×2×102
S1=100m
Step 4: Determine the distance covered by the truck for the next 20s
For next 20s the truck moved at a constant speed. Hence, a=0ms-1
Let the distance traveled for the next 20s be S2
On applying the given data in S=ut+12at2 we get,
S2=20×20+0
S2=400m
Step 5: Determine the distance covered by the truck for the last 5s
For the last 5s the truck gets stopped after applying brakes
Let the distance traveled for the last 5s be S3
On applying the equation, S=12(v+u)t
S3=1220+0×5
S3=50m
Thus, the total distance covered by the truck is S=S1+S2+S3=100+400+50=550m
Step 6: Determine the average speed of the truck
Averagespeed=TotaldistanceTotaltimetaken
=St=55035=15.7ms-1
Final 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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