Question

A van slows down as it travels up a steep hill. Its speed goes from 20m/s at the bottom of the hill to 12m/s when it reaches the top 8 seconds later. How far has the van travelled between the bottom and the top of the hill?

Answer 1

Answer

13.06 m

Explanation

The height reach ca be calculated using the one of the linear equation.

v² = u² - 2gs

where u ⇒ is the initial speed,

          v ⇒ is the final speed

        g ⇒ is the acceleration due to gravity and

       s ⇒ the height reached.

v² = u² - 2gs

12² = 20² - (2×9.8×s)

144 = 400 - 19.6s

19.6s = 400 - 144

        = 256

s = 256/19.6

    = 13.06 m

Answer 2

Answer:

d = 128 m

Explanation:

Here given that van slows down as it travels up a inclined steep hill

So here we can assume that through out the motion its acceleration will remain constant.

Now we can use kinematics to find out the distance traveled by it

As we know that acceleration is defined as

$a = \frac{v_f - v_i}{t}$

here we know that

$v_f = 12 m/s$

$v_i = 20 m/s$

time = 8 s

now we have

$a = \frac{12 - 20}{8} = -1 m/s^2$

Now in order to find out the distance it moved we can use

$v_f^2 - v_i^2 = 2 ad$

now we will plug in all above data

$12^2 - 20^2 = (2)(-1)d$

$144 - 400 = -2d$

$d = \frac{-256}{-2} = 128 m$

so it will cover total distance of 128 m