Question

The driver of a car traveling at 36 km/hr applies the brakes to decelerate uniformly. The car stops in 10 sec. Plot the speed-time graph for this period. Find the distance travelled by the car during this period by calculating the area under the graph?

Answer 1

We need to tabulate data derived from calculations and plot them.

Given,

`nu_0 = (36"km")/"h" * (10^3"m")/"km" * "h"/(3600"s") approx (10"m")/"s"`

`t = 10"s"`, and `nu = 0` (read: stops)

Recall,

`nu = nu_0 +at`

Now let's derive the deceleration which we will keep constant in our tabulation,

`=> a = (nu - nu_0)/t approx (-1"m")/("s"^2)`

Plotting the data gives us,

We don't necessarily need calculus here, because we can calculate it with recall that triangle's areas are calculate such that,

`A = 1/2bh`

Hence, the displacement of the car is approximately

`A = 1/2 (10^2) = 50"m"`

To double check,

`nu^2 = nu_0^2 + 2aDeltax`
`=> Deltax = (nu^2 - nu_0^2)/(2a) approx 50"m"`

We're correct!