Question

A rally car accelerates from 100km/h to 150km/h in 5s

what is its acceleration in
km/h/s
m/s^2

Answer 1

10 km/h/s

2.78 m/s² (2 d.p.)

Step-by-step explanation:

`\boxed{\begin{minipage}{9 cm}\underline{The Constant Acceleration Equations (SUVAT)}\\\\s = displacement in m (meters)\\u = initial velocity in m s$^(-1)$ (meters per second)\\v = final velocity in m s$^(-1)$ (meters per second)\\a = acceleration in m s$^(-2)$ (meters per second per second)\\t = time in s (seconds)\\\\When using SUVAT, assume the object is modeled\\ as a particle and that acceleration is constant.\end{minipage}}`

Acceleration in km/h/s

Given:

• u = 100 km/h
• v = 150 km/h
• t = 5 s

`\begin{aligned}\textsf{Using }v & = u+at\\\implies 150 & = 100+5a\\50 & = 5a\\a & = 10\:\sf km/h/s\end{aligned}`

Acceleration in m/s²

As:

• 1000 m = 1 km
• 3600 s = 1 hour

Therefore:

`\implies \sf 100\: km/h = (100 * 1000)/(3600)= (250)/(9)\: m/s`

`\implies \sf 150\: km/h = (150* 1000)/(3600)= (125)/(3)\: m/s`

Given:

• u = 250/9 m/s
• v = 125/3 m/s
• t = 5 s

`\begin{aligned}\textsf{Using }v & = u+at\\\implies (125)/(3)& = (250)/(9)+5a\\(125)/(9) & = 5a\\a & = (25)/(9)\\ & = 2.78\:\sf m/s^2\:\:(2\:d.p.)\end{aligned}`