Question

As a motorcycle accelerates at 5.1 m/s2, its speed changes from 16 km/h to 118 km/h. How long does this take?

Answer 1

Acceleration (a) = 5.1 m/s²
Initial speed (u) = 16 km/h ⇒
`(16*1000)/(3600)` m/s ≈ 4.5m/s
Final speed (v) =118 km/h ⇒
`(118*1000)/(3600)` m/s ≈ 32.8m/s

Distance(S) travel in that particular instant is carried out by 'Third equation of motion' i.e., v² = u² + 2aS

So, When all quantities are in S.I. unit then,
putting the values in the equation of motion,

As we have to carry out the distance covered,
2·a·S = v² - u²
S =
`( v^(2) - u^(2) )/(2a)`
Putting values in derived equation,
⇒ S =
`( (32.8)^(2) - (4.5)^(2) )/(2*(5.1))`
⇒ S =
`( 1075.84 - 20.25)/(10.2)`
⇒ S =
`(1055.59)/(10.2)`
⇒ S ≈ 103.489 m

The total distance covered in that given condition is approx. 103.289 m.

Answer 2

it takes 5.6 s

hope this helped