Question

As the traffic light turns green, a car starts from rest with a
constant acceleration of 4 m/s^2. At the same time, a motorcyclist
travelling with a constant speed of 36 km/h, overtakes and passes
the car. Find (a) How far beyond the starting point will the car
overtake the motorcyclist (b) what will be speed of the car at the
time when it overtakes the motorcycle.​

Answer 1

Answer:

When the car starts, the initial velocity = u_car = 0 m/s.

Acceleration = a_car = 4 m/s².

Distance travelled = s = ut + ½at².

⇒ s = 0*t + ½*4*t²

⇒ s = 0 + 2t²

⇒ s = 2t²

Speed of the motorcyclist = u_motorcycle = 36 km/hr = 36*5/18 = 10 m/s.

As the motorcyclist us travelling at constant speed, acceleration = a_motorcycle = 0 m/s².

Distance travelled = s = ut + ½at²

⇒ s = 10*t + ½*0*t²

⇒ s = 10t + 0

⇒ s = 10t

Equating both the equations,

⇒ s = 2t² = 10t

⇒ t²/t = 10/2

⇒ t = 5 s

So, Let's find the distance at which the car will be overtaken by the motorcyclist.

⇒ s = 2t²

⇒ s = 2*5²

⇒ s = 2*25

⇒ s = 50 m

Now, let's find the speed of the car at the time it overtakes the motorcycle.

⇒ v = u + at

⇒ v = 0 + 4*5

⇒ v = 20 m/s