Question

4
1.07
A bus starts moving with acceleration
2ms-2. A cyclist 96 m behind the bus
starts simultaneously towards the
bus at a constant speed of 20 m/s.
after what time will he be able to
overtake the bus?
С
(A) 45
14
(B)
8s
(C)
6s
144
(D)
16s​

Answer 1

Given:-

• Acceleration,a = 2 m/s²

• Distance covered,s = 96 m

• Initial velocity,u = 20 m/s

To be calculated:-

Calculate the time taken ?

Formula used:-

s = ut + 1/2 at²

Solution:-

From the second equation of motion

s = ut + 1/2 at²

★ Substituting the values in the above formula,we get:

⇒ 96 = 20 × t + 1/2 × 2 × t²

⇒ 96 = 20t + 1 × t²

⇒ 96 = 20t + t²

⇒ t² - 20t + 96

⇒ t² - 12t - 8t + 96

⇒ t ( t - 12 ) - 8 ( t - 12 )

⇒ ( t - 8 ) ( t - 12 )

⇒ t - 8 = 0 or t - 12 = 0

⇒ t = 8 or t = 12

⇒ t = 8 seconds

Option ( B ) 8 seconds