Question

A car accelerates its speed from 100km/hr to 130 km/hr in 6s. Find the acceleration of the car.​

Answer 1

Answer:

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Explanation:

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Answer 2

Answer:

1.39 m/s²

Explanation:

As per the provided information in the given question, we have been provided with the initial velocity, final velocity and time taken by the car. We have,

• Initial velocity (u) = 100 km/h
• Final velocity (v) = 130 km/h
• Time taken (t) = 6s

We've been asked to asked to calculate the acceleration of the car.

― Here, we'll be calculating the acceleration into its SI unit that is m/s². For that, we need to convert the velocities in m/s.

$\underline{\sf{ Initial \; Velocity \; : }}$

$\longrightarrow \sf{\quad { u = 100 \; km \; h^{-1}}}$

• 1 km/h = ⁵/₁₈ m/s

$\longrightarrow \sf{\quad { u = \Bigg \lgroup 100 \times \dfrac{5}{18}\Bigg \rgroup \; m \; s^{-1}}}$

$\longrightarrow \sf{\quad { u = \Bigg \lgroup \cancel{\dfrac{500}{18}}\Bigg \rgroup \; m \; s^{-1}}}$

$\longrightarrow \quad\boxed {\sf{u = 27.77\; m \; s^{-1} }}$

$\underline{\sf{ Final \; Velocity \; : }}$

$\longrightarrow \sf{\quad { v = 130 \; km \; h^{-1}}}$

• 1 km/h = ⁵/₁₈ m/s

$\longrightarrow \sf{\quad { v = \Bigg \lgroup 130 \times \dfrac{5}{18}\Bigg \rgroup \; m \; s^{-1}}}$

$\longrightarrow \sf{\quad { v = \Bigg \lgroup \cancel{\dfrac{650}{18}}\Bigg \rgroup \; m \; s^{-1}}}$

$\longrightarrow \quad\boxed {\sf{v= 36.11\; m \; s^{-1} }}$

Now, we'll calculate the acceleration of the car. Acceleration is defined as the change in velocity per unit time or the rate of change in velocity. Mathematically,

$\longrightarrow \quad \boxed{{ \textbf{\textsf{a}} = \dfrac{\textbf{\textsf{v - u}}}{\textbf{\textsf{t}}} }}$

Where,

• a denotes acceleration
• v denotes final velocity
• u denotes initial velocity
• t denotes time

$\longrightarrow \sf{\quad { a = \dfrac{(36.11 - 27.77) \; m \; s^{-1} }{6 \; s} }}$

$\longrightarrow \sf{\quad { a = \cancel{\dfrac{8.34 \; m \; s^{-1} }{6 \; s} } }}$

$\longrightarrow \quad\boxed{\textbf{\textsf{ a = 1.39 \; m }}\; \textbf{\textsf{s}}^{\textbf{\textsf{-2}}} }$

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

Therefore,

⠀⠀⠀★ Acceleration = 1.39 m/s²