Question

Starting from position s = 0 m at time t = 0 s, a particle travels on a straight-line path. The particle's velocity is given by the function v = 5 sin (4s2) m/s, where s is in meters and the argument of the sine function is unitless. Find the particle's acceleration when s = 0.25 m and s = 1.25 m.

Answer 1

acceleration is 0.2181 m/s²

acceleration is 27.05 m/s²

Step-by-step explanation:

given data

s = 0

time t = 0

velocity V = 5 sin (4s²) m/s

to find out

particle's acceleration

solution

we have given velocity = 5 sin(4s²)

and we know here that velocity =
`(ds)/(dt)`

so acceleration will be a =
`(dv)/(dt)`

put here velocity v

acceleration =
`(dv)/(dt)`

acceleration =
`(d(5sin(4s^4)))/(dt)`

acceleration = 5 cos4s² × 8s ×
`(ds)/(dt)`

acceleration = 5 cos4s² × 8s × 5 sin4s²

acceleration = 200 s ×cos4s² × sin4s²

put here s = 0.25 and s = 1.25

so

acceleration = 200× 0.25 ×cos(4×0.25²) × sin(4×0.25²)

acceleration = 0.2181 m/s²

acceleration = 200× 1.25 ×cos(4×1.25²) × sin(4×1.25²)

acceleration = 27.05 m/s²