» chapter2 » Traveling Car A car travels a certain distance along a straight roa

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» chapter2 » Traveling Car A car travels a certain distance along a straight road (in the +x direction). The distance the car travels as a function of time is shown in the figure below. When the car changes speed it does so uniformly. Select the appropriate choice for each statement. The acceleration magnitude at 36 sec is ..... the acceleration magnitude at 15 sec. At 73 sec, the speed is as high as it gets. The x-acceleration is ..... zero at 15 sec. The speed at 73 sec is ..... the speed at 10 sec. The x-acceleration is ..... zero at 70 sec . The speed is ..... zero at 26 sec.

Explanation / Answer

a) The acceleration magnitude at 36 sec is less than the acceleration magnitude at 15 sec.

Reason : At 15 sec, the car is deaccelerating with a magnitude larger than it is accelerating at 36 sec. We can see it from the change in curvature of the curve. The curve changes more sharply at 15 sec than at 36 sec. Hence, acceleration magnitude is greater at 15 sec.

b) At 73 sec, the speed is as high as it gets. False

Reason : We know that slope of the distance-time curve gives speed, So on closely examining the graph we can see that the slope of the graph is maximum during 40-60 sec, i.e., speed is maximum between 40-60 sec and hence the question is saying that speed was max at 73 sec, the above statement is False.

c)The x-acceleration is less than zero at 15 sec.

Reason: Car is deaccelerating in this interval.

d)The speed at 73 sec is less than the speed at 10 sec.

Reason: We know that slope of the distance-time curve gives speed and the higher the slope the greater the speed. So on closely examining the graph we can see that the slope of the graph at 73 sec is less than the slope of graph at 10 sec. Hence, we can say that the speed of car at 73 sec is less than the speed of car at 10 sec.

e) The x-acceleration is equal to zero at 70 sec.

Reason: At 70 sec the change in distance is directly proportional to time which implies that the car is moving with constant speed and since the car is moving with constant speed, the acceleration of the car is 0 at 70 sec.

f) The speed is equal to zero at 26 sec.

Reason: At 26 sec, the slope of the curve is 0. Hence, we can say that speed is 0 (Since, speed = slope of distance-time curve).

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