Question

A motorist is traveling on a curved section of highway of radius 762m at the speed of 96 kmph. The motorist suddenly applies the brakes, causing the automobile to slow down at a constant rate. Knowing that after 8s the speed has been reduced to 72 kmph, determine the acceleration of the automobile immediately after the brakes have been applied.

Answer 1

Answer:

-0.657

Step-by-step explanation:

Here we can go for the third equation of motion, with the help of which we can find acceleration( Negative in this case because vehicle is slowing down).

So, Third equation of motion says that:

V² - U² = 2.a.s

Where, V is the final speed, U is the initial speed a is the acceleration and s is the distance covered.

20² - 26.6² = 2.a.s...............(1)

s = ut + 1/2 a.t²

s = 26.6*8 + 0.5*a*64

s = 212.8 - 32a

Putting this value in equation 1

We get

-307.56 = 2.a.(212.8 - 32a)

It will be a quadratic equation:

64a² - 425.6a - 307.56 = 0

Solving this, we get

a=7.3076,−0.6576.

Since we want only negative acceleration, because vehicle is slowing down. Therefore final acceleration = - 0.657