Albert is riding his scooter at a velocity of 80km/h, when he sees an old woman crossing the road 45m away. He immediately steps hard on the brakes to get the maximum deceleration of 7.5m/s^2. How far will he go before stopping?
Do you need to do this with claculus or with physics formulas?
FORMULA METHOD
Here are the motion formulas that you should learn.
\(80km/hour =80000/(60*60) m/sec=800/36 m/sec=800/36 m/sec=22.\dot2 m/s\\\)
u=22.2 m/s
v=0
t=?
a=-7.5
s=?
I want stopping distance, s and i do not have t so that means I can use the last formula
\(v^2=u^2+2as\\ 0=22.\dot2^2+2*-7.5*s\\ s\approx 32.92m\)
The scooter can stop in 33m so Albert should stop in time.
NOW USING CALCULUS
\( \ddot x=-7.5\\ \dot x = -7.5t+22.\dot2\\ x=\frac{-7.5t^2}{2}+22.\dot2t\\ x=-3.75t^2+22.\dot2t \)
When \(\dot x = 0\)
\(0=-7.5t+22.\dot2\\ t\approx2.963sec\\ x\approx-3.75*2.963^2+22.\dot 2*2.963\\ x\approx 32.92m \)
Fortunately the answers are the same :)