Question

on a long straight free road a vehicle starts from rest and accelerates uniformly to a speed of 30m/s in 20s. find the acceleration of vehicle.also find the displacement of the vehicle in these 20s.​

Answer 1

Working out:

The above question is based on Kinematics more specifically applications of equations of motion which are as follows:

• v = u + at
• s = ut + 1/2 at²
• v² = u² + 2as

Here, symbols have their usual meanings.

Given data in the Question:

• Initially at rest
• Finally attained a speed of 30 m/s
• Time taken = 20s

To FinD:

• Acceleration of the body.
• Distance travelled in 20s

1) Finding Acclearation:

• v = 30 m/s.
• u = 0 m/s
• t = 20 s

By using 1st equation of motion,

➝ v = u + at

➝ 30 = 0 + a(20)

➝ 20a = 30

➝ a = 1.5 m/s²

So, acceleration of the body:

$\large{ \boxed{ \bf{ \blue{a = 1.5 \: m {s}^{ - 2} }}}}$

2) Finding distance travelled:

• u = 0 m/s
• t = 20s
• a = 1.5 m/s²

By using 2nd equation of motion,

➝ s = ut + 1/2 at²

➝ s = 0(20) + 1/2 × 1.5 × 20²

➝ s = 0 + 200 × 1.5

➝ s = 300 m

So, distance travelled by the body:

$\large{ \boxed{ \bf{ \blue{s = 300 \:m }}}}$

And we are done !!

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