Question

Car A and B start a race from rest. Car A starts with an acceleration of...

Car A and B start a race from rest. Car A starts with an acceleration of 100 m/s^2 and after 10s increases with acceleration to 200 m/s^2. Car B starts with an acceleration of 50 m/s^2 and after 5s increases the acceleration to 300 m/s^2.

1) What is the distance between cars after 1s

2) What is the velocity of each car after 1s

3) After 30 seconds which car is ahead?

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Answer #1

The initial velocity of the cars are zero, the following equations of motion were used,

(1) Distance travelled by the car A in 1 second is,

Distance travelled by the car B in 1 second is,

(2) Velocity of the car A in 1 second is,

Velocity of the car B in 1 second is,

(3) Since acceleration is different after the first 10 seconds, we have to calculate distances in two parts.

Distance travelled and velocity of car A in 10 seconds is,

Hence distance travelled by the car A in next 20 seconds is,

Hence the total distance travelled is 65000 m.

Distance travelled and velocity of car B in 10 seconds is,

Hence distance travelled by the car B in next 20 seconds is,

Hence the total distance travelled is 72500 m.

Therefore car B is ahead.

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