Answer to Question #309301 in Physics for Elijah

Question

A car is speeding up and has an instantaneous velocity of 1.0 m/s in the +x-direction when a stopwatch reads 10.0 s. It has a constant acceleration of 2.0 m/s² in the x-direction. (a) What change in speed occurs between t = 10.0 s and t = 12.0 s? (b) What is the speed when the stopwatch reads 12.0 s?

Answer 1

a) The change in speed is given as follows, according to the kinematic equation:

$$\Delta v = a\Delta t$$

where $a= 2m/s^2$ is the acceleration, and $\Delta t = 12s-10s = 2s$ is the time interval. Thus, obtain:

$$\Delta v = 2m/s^2\cdot 2s = 4m/s$$

b) The speed at 12s is:

$$v = v_0 + \Delta v$$

where $v_0 = 1m/s$ is the initial speed. Thus, have:

$$v = 1m/s + 4m/s = 5m/s$$

Answer. a) 4m/s, b) 5m/s.