Question

A car moving along the positive x-axis with a uniform velocity of 6 m/s passes a biker at a signal. The
biker who was riding at a velocity of 5 m/s decides to overtake the car and starts accelerating
uniformly. She finally overtakes the car 30 meters away. Find the biker’s acceleration.

Answer 1

Answer:

The acceleration of the biker is 0.4 m/s²

Explanation:

Velocity of car is 6 m/s and initial velocity of biker is 5 m/s. Let the required acceleration be a m/s²

The whole story starts when the car just overtakes the biker ( You may think that the biker needs some time to react and to accelerate, but it is neglected here).

Let the time taken by the biker to overtake the car be t seconds,

Now both car and biker have moved a distance of 30 metres in t seconds.

Therefore 6=30/t ( for car)

Hence t=5 seconds

which means through constant acceleration and with initial velocity 5 m/s the biker overtakes(travels 30 metres) the car in 5 seconds.

From the equation  $s=ut+\frac{1}{2} at^{2}$

  30=5(5)+a5*5/2 ( for biker)

⇒25a/2=5

⇒5a/2=1

⇒a=2/5 m/s² or 0.4 m/s²