Chapter 2, Problem 49P

(a)

To determine

The time when velocity is greatest.

Answer to Problem 49P

Velocity is at peak at $t\approx 50\sec$

Explanation of Solution

Given:

The velocity-time graph is shown below.

  

Calculation:

For the given velocity-time graph, it is observed that peak value of velocity is $v=38\text{m/s}$ . It lies approximately at 50 seconds.

Conclusion:

Therefore, velocity is at peak at $t\approx 50\sec$

(b)

To determine

To find: The time period, for the constant velocity.

Answer to Problem 49P

Velocity is constant for

  $t=90\mathrm{s}\text{to}t=108\mathrm{s}$

Explanation of Solution

Given:

The velocity-time graph is shown below.

  

Calculation:

From the given graph, it is observed that the curve is a flat line or shows a constant value from time range approximately from 90 seconds to 108 seconds. It means between this time interval train is moving in a straight line with the same speed irrespective of time.

Conclusion:

Therefore, velocity is constant during $t=90\mathrm{s}\text{to}t=108\mathrm{s}$

(c)

To determine

To find: The time period, for the constant acceleration.

Answer to Problem 49P

Acceleration is constant from,

  $t=0\sec \text{to}t=38\sec$ , $t=62\sec \text{to}t=83\sec$

Explanation of Solution

Given:

The velocity-time graph is shown below.

  

Formula used:

Acceleration is calculated as $a=\frac{\Delta v}{\Delta t}$

Calculation:

As shown in the graph, constant acceleration is obtained by deducing the slope of the velocity-time graph. Here, acceleration is constant in two different intervals, firstly in the starting period of $t=0\sec \text{to}t=20\sec$ , then in a downward motion at $t=62\sec \text{to}t=83\sec$

Conclusion:

Therefore, acceleration is constant in $t=0\sec \text{to}t=20\sec$ and $t=62\sec \text{to}t=83\sec$

(d)

To determine

To find: The time for the greatest acceleration.

Answer to Problem 49P

The magnitude of the acceleration is at a peak at $t\approx 62s-t\approx 83\mathrm{s}$

Explanation of Solution

Given:

The velocity-time graph is shown below.

  

Calculation:

As shown in the graph, The magnitude of the acceleration is greatest when the slope is at a peak i.e. at $t\approx 62s-t\approx 83\mathrm{s}$

Conclusion: The magnitude of the acceleration is at a peak at $t\approx 62s-t\approx 83\mathrm{s}$