A 100-g toy car is propelled by a compressed spring that starts it moving. The car follows the curved track in Figure 7.39. Show that the final speed of the toy car is 0.687 m/s if its initial speed is 2.00 m/s and it coasts up the frictionless slope, gaining 0.180 m in altitude.

Solution 20PE

The toy car moves up the slope and gains a height. This gain in height will result in the change in potential energy for the toy. At the start of its motion, the toy car will have a greater velocity. But as it will continue to move upward, it will slow down. So, there will be a change in its kinetic energy. We are required to calculate the speed of the toy when it reaches the height of 0.180 m.

Step 1 of 2

Initial height of the toy is zero. So, the initial potential energy of the toy is also zero.

The initial speed of the toy m/s

Final height of the toy m

We are required to show that the final speed of the toy is 0.687 m/s.