## Initial Velocity

A motorcycle is accelerating at a constant rate of 5 ft/sec^2. It travels 100 ft while its speed changes to 60 ft/s. What is the initial velocity in ft/s?

##
__
__**Expand Hint**

**Expand Hint**

$$$v^2=v_0^2+2a_0(s-s_0)$$$

where
$$v$$
is the velocity along the direction of travel,
$$v_0$$
is the velocity at time
$$t_0$$
,
$$a_0$$
is constant acceleration,
$$s$$
is the displacement at time
$$t$$
along the line of travel, and
$$s_0$$
is the displacement at time
$$t_0$$
.

##
__
__**Hint 2**

**Hint 2**

Solve for
$$v_0$$

For constant acceleration, the equation for velocity as a function of position:

$$$v^2=v_0^2+2a_0(s-s_0)$$$

where
$$v$$
is the velocity along the direction of travel,
$$v_0$$
is the velocity at time
$$t_0$$
,
$$a_0$$
is constant acceleration,
$$s$$
is the displacement at time
$$t$$
along the line of travel, and
$$s_0$$
is the displacement at time
$$t_0$$
.

Solving for initial velocity:

$$$(60ft/s)^2=v_0^2+2(5\frac{ft}{s^2})(100ft)$$$

$$$3,600ft^2/s^2=v_0^2+1,000ft^2/s^2$$$

$$$v_0=\sqrt{(3,600ft^2/s^2-1,000ft^2/s^2)}=\sqrt{2,600ft^2/s^2}=51\:ft/s$$$

51 ft/s

Similar Problems from FE Sub Section:

037. Motorcycle's Velocity

088. Constant Acceleration

316. Jet Ski

321. Traveling Train

322. Aircraft Carrier

487. G-Force

Similar Problems from FE Section:

018. A Pebble on a Mountain

030. Newton's 2nd Law

037. Motorcycle's Velocity

088. Constant Acceleration

122. Roller Coasters

158. A Train's Velocity

165. Velocity Plots

313. Projectile Motion

316. Jet Ski

321. Traveling Train

322. Aircraft Carrier

325. Pebble Off a Building

394. Acceleration

412. Hill Bomb

444. Electron Motion

487. G-Force

488. Block Speed

**Constant Acceleration**037. Motorcycle's Velocity

088. Constant Acceleration

316. Jet Ski

321. Traveling Train

322. Aircraft Carrier

487. G-Force

Similar Problems from FE Section:

**Particle Kinematics**018. A Pebble on a Mountain

030. Newton's 2nd Law

037. Motorcycle's Velocity

088. Constant Acceleration

122. Roller Coasters

158. A Train's Velocity

165. Velocity Plots

313. Projectile Motion

316. Jet Ski

321. Traveling Train

322. Aircraft Carrier

325. Pebble Off a Building

394. Acceleration

412. Hill Bomb

444. Electron Motion

487. G-Force

488. Block Speed