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Q4 OQ

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Physics For Scientists & Engineers
Found in: Page 137

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Short Answer

The driver of a speeding truck slams on the brakes and skids to a stop through a distance d. On another trial, the initial speed of the truck is half as large. What now will be the truck’s skidding distance? (a) 2d (b) 2d (c) d (d) d/2 (e) d/4

The stopping distance of the truck for half the initial speed is d4 , and Option (e) is correct.

See the step by step solution

Step by Step Solution

Step 1: Identification of given data

The stopping distance for the first case is d1=d .

The initial speed in the second case is v=u2

The work-energy theorem is used to find the stopping distance for half the initial speed in the second case.

Step 2: Determine the stopping distance in the second case

Apply the work-energy theorem for the truck in the first case.

12mu2=F·d1......1

Here, m is the mass of the truck, u is the initial speed of the truck, and F is the braking force.

Apply the work-energy theorem for the truck in the second case.

12mv2=F·d212mu22=F·d21412mu2=F·d2......

Divide equation (2) by equation (1) to find the stopping distance of the truck in the second case.

1412mu212mu2=F·d2F·d1d2d=14d2=d4

The stopping distance of the truck for half the initial speed is d4 .

Therefore, the stopping distance of the truck for half the initial speed is d4, and Option (e) is correct.

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