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Question

The equation of motion of a car is ,s=t2-2t where t is measured in hours and s is measured in kilometers. If the distance traveled by car is 15 km, find the velocity of the car


A

4kmh

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B

2kmh

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C

3kmh

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D

8kmh

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Solution

The correct option is D

8kmh


Step 1: Given Data:

Distances=15km

The equation for the motion of the car, s=t2-2t·····1

Step 2: Formula used:

Velocity is the rate of change of displacement that is-

v=dsdt

Step 3: Calculation of the velocity of the car:

The distance traveled by car is 15km. Substitute the value of distance in equation 1 to obtain the time taken to travel this distance.

t2-2t=15t2-2t-15=0t2-5t+3t-15=0tt-5+3t-5=0t-5t+3=0t=5,-3

-3 can be neglected because time can't be negative. So

t=5hrs

Differentiate equation 1 with respect to time to get the velocity,

dsdt=2t-2v=2t-2.......(2)

Substitute the value of t=5hrs in equation (2) to compute the value of velocity.

v=2×5-2v=8kmhr

Hence, option D is the correct answer.


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