Constant Acceleration

#088 / Dynamics Easy

A car accelerates at a constant rate of 12 m/sec^2. The car travels 140 meters while its speed changes to 60 m/sec. What is the initial velocity?

Expand Hint
$$$v^{2}=v_{o}^{2}+2a(S-S_{o})$$$
where $$v$$ is the velocity along the direction of travel, $$v_o$$ is the velocity at time $$t_0$$ , $$a$$ is constant acceleration, $$S$$ is the displacement at time $$t$$ along the line of travel, and $$S_o$$ is the displacement at time $$t_0$$ .
Hint 2
Solve for initial velocity, $$v_o$$ .
For constant acceleration, the equation for velocity as a function of position:
$$$v^{2}=v_{o}^{2}+2a(S-S_{o})$$$
where $$v$$ is the velocity along the direction of travel, $$v_o$$ is the velocity at time $$t_0$$ , $$a$$ is constant acceleration, $$S$$ is the displacement at time $$t$$ along the line of travel, and $$S_o$$ is the displacement at time $$t_0$$ .
Solving for initial velocity:
$$$v_{o}^{2}=v^{2}-2a(S-S_{o})$$$
$$$v_{o}^{2}=(60\:m/sec)^{2}-2(12\:m/sec^2)(140\:m)$$$
$$$v_{o}^{2}=3,600\:m^2/sec^{2}-3,360\:m^2/sec^2$$$
$$$v_{o}=\sqrt{240\:m^2/sec^2}= 15.5\:m/sec$$$
15.5 m/s


☕️ Donate to keep your study guide and instructor running!
🚨 [Beta] Test your FE exam readiness with a timed quiz!
☝️ Take the survey to help us improve!

< Prev #087

random #

#089 Next >