Question

PLEASE HELP: A car is traveling at 72.0 km/h, when the driver notices an overturned truck blocking the road 95.0 m ahead. The car travels at 72.0 km/h for 0.50 s before the driver applies the brakes. (Please show work).

(a) How far does the car travel in that 0.50 s?

(b) If the car has an acceleration of -2.50 m/s², will it be able to stop before reaching the truck? If not, how fast is the car traveling when it collides with the truck?

Answer 1

10 m

Yes, the car will be able to stop before it reaches the truck.

Step-by-step explanation:

`u=\text{Initial velocity of the car}=(72)/(3.6)=20\ \text{m/s}`

`t=\text{Time}=0.5\ \text{s}`

`s=\text{Displacement}`

From the laws of motion we have

`s=ut+(1)/(2)at^2\\\Rightarrow s=20* 0.5+0\\\Rightarrow s=10\ \text{m}`

The car will travel 10 m in 0.5 seconds

`a=\text{Acceleration}=-2.5\ \text{m/s}^2`

`v^2-u^2=2as\\\Rightarrow s=(v^2-u^2)/(2a)\\\Rightarrow s=(0^2-20^2)/(2* -2.5)\\\Rightarrow s=80\ \text{m}`

Total distance required for the car to stop is 10+80 = 90 m. So, the car will be able to stop before it reaches the truck.