Question

If a vehicle accelerates with the acceleration of 3.0m/s2 starting from rest. Then, how long will it take to go 3000 m ? find final velocity also​

Answer 1

Hope it helps u......... refer image solution............

Answer 2

Answer:-

Given:-

• Initial velocity (u) = 0 m/s [Rest]
• Acceleration (a) = 3 m/s²
• Distance travelled (s) = 3000 m or, 3 km.

To Find: Time it will take to reach 3 kilometres and it's final velocity,

OR: To find (t) and (v).

We know,

s = ut + ½at² and

v = u + at

where,

• s = Distance travelled,
• u = Initial velocity,
• t = Time taken,
• a = Acceleration and
• v = Final velocity.

Finding time taken:-

Here,

s = ½at²

3000 m = ½(3 m/s²)(t)²

→ 1.5 m/s² × t² = 3000 m

→ t² = (3000 m)/(1.5 m/s²)

→ t² = 2000 s²

→ t = √(2000 s²)

→ t = 10√(20) s

(→ t ≈ 44.7 s)

NOW, finding it's final velocity:-

Here,

v = at

→ v = (3 m/s²)[10√(20) s]

→ v = 30√(20) m/s

(→ v ≈ 134 m/s)

∴ Time it will take to cover 3 kilometers is approximately 45 seconds and the final velocity is about 134 m/s.