Question

A motorcycle and a car start from rest from the same place at the same time and travel in the same direction.The motorcycle accelerates at 1.0 ms up to a speed of 36 km/h and the car at 0.5 ms up to a speed of 54 km/h. The time at which the car would overtake the motorcycle is
(a) 20 s
(b) 25 s
(c) 30 s
(d) 35 s.

here I am getting two correct answers (a)20 s & (b)35s......clarify my doubt.​

Answer 1

Solution:

Distance from starting point, where bike reaches its final speed, 10 m/s, is given by:

$\implies$ $\boxed{\sf{v^{2} = 2 \times a \times s}}$

Hence,

$\implies$ s = v^2 / (2a)

$\implies$ s = 100/2

$\implies$ s = 50 m

Time t1 for the bike to reach final velocity:

$\implies$ v/a

$\implies$ 10/1

$\implies$ 10 s

Distance from starting point, where car reaches, it's final speed, 15m/s, is given by:

$\implies$ $\boxed{\sf{v^{2} = 2 \times a \times s}}$

Hence,

$\implies$ s = v^2 / (2a)

$\implies$ s = 225 / (2×0.5)

$\implies$ s = 225 m - - - - (1)

Time t2 for the car to reach final velocity:

$\implies$ v/a

$\implies$ 15/0.5

$\implies$ 30 s

In this,

30 s duration of car = Initial 50 m in 10 s + 20 s with uniform speed 10 m/s

$\implies$ 50 + 20 × 100 = 250 m - - - - (2)

From (1) and (2), we know that, after 30 s, the distance between car and bike = 25 m

That is,

After 30 s, both bike and car are moving with uniform speed. Car speed is 15 m/s and bike speed is 10 m/s.

Hence additional time to cover this 25 m gap:

$\implies$ 25 / (15-10)

$\implies$ 25 / 5

$\implies$ 5 s

Total time is: 30+5 = 35 s

Therefore:

Correct option: (d) 35 s

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Answered by: Niki Swar, Goa❤️

Answer 2

Answer:d. 35s

Explanation: