Question

At t = 0 the components of a radio-controlled car's velocity are vx = 0.5 m/s and vy = 1.2 m/s. Find the components of the car's velocity at t = 4.1 s, given that the components of its average acceleration during this period are ax = 2 m/s2 and ay = -1 m/s2.

Answer 1

vx' = 8.7 m/s

vy' = - 2.9 m/s

Step-by-step explanation:

The average acceleration during a time period is given by the formula:

a = (v' - v)/(t' - t)

where,

a = average acceleration

v' = Final Velocity

v = Initial Velocity

t' = Ending Time

t = Starting Time

Now, for x-component of velocity:

a = ax = 2 m/s²

v' = vx' = ?

v = vx = 0.5 m/s

t' = 4.1 s

t = 0 s

Therefore,

2 m/s² = (vx' - 0.5 m/s)/(4.1s - 0s)

(2 m/s²)(4.1 s) = vx' - 0.5 m/s

8.2 m/s + 0.5 m/s = vx'

vx' = 8.7 m/s

For y- component of velocity:

a = ay = -1 m/s²

v' = vy' = ?

v = vy = 1.2 m/s

t' = 4.1 s

t = 0 s

Therefore,

- 1 m/s² = (vy' - 1.2 m/s)/(4.1s - 0s)

(- 1 m/s²)(4.1 s) = vy' - 1.2 m/s

- 4.1 m/s + 1.2 m/s = vy'

vy' = - 2.9 m/s