Question

A bus travelling at 30m/s along a straight road passes throu a stationary taxi cab.the can begins to move 5seconds later within a uniform acceleration of 2metres per seconds square in the same direction as the bus.1.calculate the time taken by the cab to meet the bus.2.distance the cab has travelled to catch-up with the bus

Answer 1

(1) The time taken by the cab to meet the bus is 18.96 seconds.

(2) The distance the cab has travelled to catch-up with the bus is 718.96 m.

Distance between the bus and the cab

The distance between the bus and the cab when the cab begins to move is calculated as follows;

D = speed x time

D = 30 m/s x 5 s

D = 150 m

Velocity of the cab

The velocity of the cab when it begins to move is calculated as follows;

v = at

(v - 30)t = D

(at - 30)t = 150

(2t - 30)t = 150

2t² - 30t = 150

2t² - 30t - 150 = 0

solve the quadratic equation using formula method

t = 18.96 seconds

Distance traveled by the cab

D =  vt

D = 2t²

D = 2(18.96²)

D = 718.96 m

Thus, the time taken by the cab to meet the bus is 18.96 seconds. The distance the cab has travelled to catch-up with the bus is 718.96 m.

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