Question

An Automobile travelling with an initial
velocity of 40 ms comes to rest after
travelling. a distance of 100m, assuming the
retardation to
be uniform. Find its
value, What time does it take to cover
the distance?

Answer 1

Answer:

Retardation = -8 m/s²

Time taken = 5 s

Explanation:

Given:

• Initial velocity = 40 m/s
• Final velocity = 0 m/s
• Distance travelled = 100 m

To Find:

• Retardation
• Time taken to cover the distance

Solution:

Let us first find the retardation of the automobile.

By the third equation of motion we know that,

v² - u² = 2as

where v = final velocity

u = initial velocity

a = acceleration/retardation

s = distance travelled

Substitute the data,

0² - 40² = 2 × a × 100

-1600 = 200 a

a = -1600/200

a = -8 m/s²

Hence the retardation of the automobile is -8 m/s².

Here acceleration is negative since it is retardation or deceleration.

Now finding the time taken,

By the first equation of motion,

v = u + at

where v = final velocity

u = initial velocity

a = acceleration

t = time taken

Substitute the data,

0 = 40 + -8t

t = -40/-8t

t = 5 s

Hence the time taken by the automobile to cover the distance is 5 s.