Question

A bike rider pedals with a constant acceleration of 1.2 m/s^2 to reach a velocity of 7.5 m/s north. Find his initial velocity if the displacement was 19 meters.

Answer 1

The initial velocity of the bike rider, who pedals with a constant acceleration of 1.2 m/s^2 to reach a velocity of 7.5 m/s with a displacement of 19 meters, is 3.26 m/s north.

Step-by-step explanation:

To find the initial velocity of a bike rider who pedals with a constant acceleration, we can use the kinematic equation:

v2 = u2 + 2as

where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement. Given a = 1.2 m/s2, v = 7.5 m/s north, and s = 19 meters, we need to rearrange the equation to solve for u:

u = sqrt(v2 - 2as)

Substituting the given values:

u = sqrt((7.5 m/s)2 - 2(1.2 m/s2)(19 m))
= sqrt(56.25 m2/s2 - 45.6 m2/s2)
= sqrt(10.65 m2/s2)
= 3.26 m/s

The initial velocity of the bike rider is therefore 3.26 m/s north.