Question

Numerical based on the equation of motion

1.Find the initial velocity of a bike which is stopped in 105 by applying bakers.the retardation due to brakes is 2.5m/s.
2
A body starting from rest travels with uniforms acceleration .it travels 100m in 5 second then what is the value of acceleration
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Answer 1

Correct Ques 1.

Find the initial velocity of a bike which is stopped in 10 sec by applying bakers. The retardation due to brakes is 2.5m/s².

Ans.

Given that, time (t) = 10 sec and retardation (-a) = -2.5 m/s² and final velocity (v) = 0 m/s (As brakes are applied)

We have to find the initial velocity (u) of the bike.

Using First Equation of Motion

v = u + at

→ 0 = u + (-2.5)(10)

→ -u = -25

→ u = 25 m/s

Therefore, Initial velocity of the bike is 25 m/s.

$\rule{100}1$

Ques 2.

A body starting from rest travels with uniforms acceleration. It travels 100m in 5 seconds then what is the value of acceleration.

Ans.

Given that, initial velocity (u) = 0 m/s, distance (s) = 100 m and time (t) = 5 sec

We have to find the acceleration (a).

Now,

s= ut + 1/2 at²

→ 100 = 0(5) + 1/2 a(5)²

→ 100 = 1/2 × 25a

→ 200 = 25a

→ 8 = a

Therefore, acceleration of the body is 8 m/s².

Answer 2

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Correct question 1:-

Find the initial velocity of a bike which is stopped in 10 s by applying bakers. The retardation due to brakes is 2.5 m/s².

Solution :-

♣ Time (t) = 10 s

♣ Redardation(a) = -2.5 m/s²          ('a' is negative as the velocity decreases)

♣ Final velocity(v) = 0 m/s              (As the bike comes to rest)

We know,

v = u + at

Putting the values in the equation:

0 = u + 10(-2.5)

⇒0 = u - 25

$\bold{\boxed{\implies u = 25\ m/s}}$

∴So, the initial velocity of the bike was 25 m/s.

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Question 2:-

A body starting from rest travels with uniforms acceleration. It travels 100 m in 5 seconds. Then what is the value of acceleration

?

Solution:-

Initial velocity(u) = 0 m/s          (As the body starts from rest)

Distance travelled (s) = 100 m

Time (t) = 5 s

We know,

s = ut + 1/2 at²

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Putting the values in the equation:

100 = 0*5 + 1/2 a(5)²

⇒100 = 0 + 1/2 25a

⇒200 = 25a

⇒a = 200/25

${\bold{\boxed{\implies a = 8\ m/s\²}}$

∴So, the acceleration of the body is 8 m/s².

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