Question

Q6 A motorcyclist heading east through a small Iowa city accelerates after he passes the signpost marking the city limits. His acceleration is a constant 4.0 m/S2. At time t = 0 he is 5.0 m east of the signpost, moving east at 15 m/s. (a) find his position and velocity at time t = 2.0 s. (b) Where is the motorcyclist when his velocity is 25 m/s?

Answer 1

Given :

• constant acceleration of motorcyclist, a = 4 m/s²
• position of motorcyclist at time t = 0 , x₀ = 5 m  east of signpost
• initial velocity of motorcyclist, v₀ = 15 m/s

To find :

• position of motorcyclist at  t = 2 s , x = ?
• velocity of motorcyclist a t  t = 2 s , vₓ = ?
• position of motorcyclist when its velocity will be 25 m/s , x' = ?

Knowledge required :

First equation of kinematics

• vₓ = v₀ + a t

Second equation of kinematics

• x = x₀ + v₀ t + 1/2 a t²

Third equation of kinematics

• vₓ² = v₀² + 2 a ( x - x₀ )

[ where vₓ is final velocity (velocity acquired after a time t ), v₀ is initial velocity , t is time taken ,  a is constant acceleration , x is distance covered (after a time t) , and x₀ is initial position of  any body ]

Solution :

Calculating velocity motorcyclist at a time t = 2 sec ; vₓ = ?

Using first equation of kinematics

→ vₓ = v₀ + a t

→ vₓ = ( 15 ) + ( 4 ) ( 2 )

→ vₓ = 15 + 8

→ vₓ = 23 m/s

therefore,

• velocity of motorcyclist after 2 seconds will be 23 m/s .

Calculating position of motorcyclist at time t = 2 sec ; x = ?

Using second equation of kinematics

→ x = x₀ + v₀ t + 1/2 a t²

→ x = ( 5 ) + ( 15 ) ( 2 ) + 1/2 ( 4 ) ( 2 )²

→ x = 5 + 30 + 8

→ x = 43 m

therefore,

• position of motorcyclist after 2 seconds will be 43 m east from the signpost.

Calculating position of motorcyclist when its velocity will be v = 25 m/s ; x' = ?

Using third equation of kinematics

→ v² = v₀² + 2 a ( x' - x₀ )

→ ( 25 )² = ( 15 )² + 2 ( 4 ) ( x' - 5 )

→ 625 - 225 = 8 ( x' - 5 )

→ 400 / 8 = x' - 5

→ x' = 50 + 5

→ x' = 55 m

Therefore,

• position of motorcyclist when its velocity becomes 25 m/s will be 55 m east from the signpost.

Answer 2

Answer:

23 m/s = v at t

43 m = p after t

55 m = p when v is 23m/s (E)

Explanation:

A motorcyclist travelling east through a small town accelerates at a constant speed of 4.0 m/s² after leaving the town limits. At time t=0, he is 5.0 m east of the town entrance sign and moving east at 15 m/s. 1.

Find the position and the speed at time t=2s. 2.

2. where is the motorcyclist when the speed is 25 m/s?