Question

an object, initially at rest, is accelerated by a constant force. which graphs show the variation with time t of the kinetic energy and the variation with time t of the speed of the object? a. kinetic energy speed b. kinetic energy speed c. kinetic energy speed

Explanation:

Step1: Recall equations of motion

For an object with initial velocity $u = 0$ and constant acceleration $a$, the speed - time relation is $v=u + at$. Since $u = 0$, $v=at$. So speed $v$ is directly proportional to time $t$ ($v\propto t$), and the speed - time graph is a straight - line passing through the origin with a non - zero slope.

Step2: Recall kinetic energy formula

The kinetic energy formula is $K=\frac{1}{2}mv^{2}$. Substituting $v = at$ into the kinetic energy formula, we get $K=\frac{1}{2}m(at)^{2}=\frac{1}{2}ma^{2}t^{2}$. Since $m$ and $a$ are constants, $K\propto t^{2}$, and the kinetic energy - time graph is a parabola passing through the origin.

Answer:

A. kinetic energy graph is a parabola passing through the origin and speed graph is a straight - line passing through the origin.