Question

A body starting from rest travels with uniform acceleration. If it travels 100m in 5s, what is the value of acceleration?

Answer 1

Answer- The above question is from the chapter 'Kinematics'.

Some important terms and formulae:-

1. Velocity- It is the displacement per unit time.

S.I. Unit of Velocity- m/s

It is a vector quantity as it possesses magnitude and direction.

2. Acceleration- It is the rate of change of velocity.

S.I. Unit of Acceleration- m/s²

It is also a vector quantity.

Negative acceleration is called retardation.

3. Distance- It is the path length transversed by an object.

S.I. Unit of Distance- m

It is a scalar quantity.

4. Displacement- It is the shortest distance between the initial and final point.

S.I. Unit of Displacement- m

It is a vector quantity.

5. Equations for uniformly accelerated motion-

Let u = Initial velocity of a particle

v = Final velocity of a particle

t = Time taken

s = Distance travelled in the given time

a = Acceleration

1) v = u + at

2) s = $\frac{1}{2}$ at² + ut

3) v² - u² = 2as

Given question: A body starting from rest travels with uniform acceleration. If it travels 100 m in 5 s, what is the value of acceleration?

Answer: We are given that,

u = 0 m/s (Body was at rest)

s = 100 m

t = 5 s

Using 2nd equation of motion,

s = $\frac{1}{2}$ at² + ut

100 = $\frac{1}{2}$ a × 5² + 0 × 5

100 = $\frac{1}{2}$ a × 5²

100 ÷ 25 = $\frac{1}{2}$ a

a = 4 × 2

a = 8 m/s²

∴ Value of acceleration = 8 m/s².

Answer 2

Answer:

⠀⠀⠀⋆ Initial Velocity (u) = 0 m/s

⠀⠀⠀⋆ Distance Travelled (s) = 100 m

⠀⠀⠀⋆ Time Taken (t) = 5 seconds

⠀⠀⠀⋆ Acceleration (a) = ?

$\underline{\bigstar\:\textsf{Using Second Equation of Motion :}}$

$:\implies\sf s = ut+\dfrac{1}{2}at^2\\\\\\:\implies\sf 100=(0 \times 5)+\bigg\lgroup\dfrac{1}{2} \times a \times (5)^2\bigg\rgroup\\\\\\:\implies\sf 100 = \dfrac{1}{2} \times a \times 25\\\\\\:\implies\sf \dfrac{100 \times 2}{25} = a\\\\\\:\implies\sf 4 \times 2 = a\\\\\\:\implies\underline{\boxed{\sf a = 8\:ms^{ - 2}}}$

⠀

$\therefore\:\underline{\textsf{Hence, the value of Acceleration is \textbf{8 ms ^{\text{-2}} }}}.$