Question

starting from rest 100m in 5s with uniform acceleration. Find the acceleration of the car​

Answer 1

Answer:

$\boxed{\mathfrak{Acceleration = 8 \ m/s^2}}$

Given:

Initial velocity (u) = 0 m/s (Starts from rest)

Displacement (s) = 100 m

Time taken (t) = 5 s

Explanation:

$\rm From \: 2^{nd} \: equation \: of \: motion \: we \: have: \\ \boxed{ \bold{s = ut + \dfrac{1}{2} a {t}^{2}}}$

a → Acceleration

By substituting values in the equation we get:

$\rm \implies 100 = 0 \times 5 + \dfrac{1}{2} \times a \times {5}^{2} \\ \\ \rm \implies 100 = \dfrac{25}{2} a \\ \\ \rm \implies a = \dfrac{2}{25} \times 100 \\ \\ \rm \implies a = 2 \times 4 \\ \\ \rm \implies a = 8 \: m {s}^{ - 2}$

Answer 2

Answer :

➥ The Acceleration of a car = 8 m/s²

Given :

➤ Distance travelled by a car = 100 m

➤ Time taken by a car = 5 sec

To Find :

➤ Acceleration of a car = ?

Required Solution :

❒ In the above Question, we are provided that A car is starting from rest 100m in 5s with uniform acceleration. That means Initial velocity is 0 m/s because the car starting from rest, Distance covered by a car is 100 m, and time taken by a car is 5 sec.

Now, we have also the Initial velocity of a car,

• Initial velocity of a car (u) = 0 m/s

We can find Acceleration of a car by using the second equation of motion which says s = ut + ½ at².

Here,

• s is the Distance in m.
• u is the Initial velocity in m/s.
• t is the Time taken in second.
• a is the Acceleration in m/s².

✎ So let's find Acceleration (a) !

⇛ s = ut + ½ at²

⇛ 100 = 0 × 5 + ½ a × 5²

⇛ 100 = 0 + ½ a × 25

⇛ 100 = 0 + 1 × a × 12.5

⇛ 100 = 0 + a × 12.5

⇛ 100 = 0 + 12.5a

⇛ 100 = 12.5a

⇛ 100/12.5 = a

⇛ 8 = a

⇛ a = 8 m/s²

║Hence, the Acceleration of a car is 8 m/s².║

$\:$

Formulae of Acceleration :

⪼ $\sf{a = \dfrac{v - u}{t}}$

⪼ $\sf{a = \dfrac{Change\: in\: velocity }{time}}$

⪼ $\sf{a = \dfrac{v_{f} - u_{i}}{t}}$

Where,

• a is the Acceleration in m/s².
• v is Final velocity in m/s.
• u is Initial velocity in m/s.
• t is Time taken in second.
• $\sf v_{f}$ is Final velocity in m/s.
• $\sf u_{f}$ is Initial velocity in m/s.

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