Question

motorcyclist travelling along a straight path at a velocity of 5 m.s-1 accelerates his bike for 10 seconds. If the acceleration produced was 2 m.s-2, determine his displacement in those 10 seconds.

Answer 1

Given :

➳ Initial velocity = 5m/s

➳ Acceleration = 2m/s²

➳ Time of journey = 10s

To Find :

⟶ Displacement of motorcyclist after the given interval of time.

SoluTion :

➝ Here, Acceleration has said to be constant throughout the period of motion, so we can easily apply equation of kinematics to solve this question.

➝ Second equation of kinematics :

$\bigstar\:\boxed{\bf{s=ut+\dfrac{1}{2}at^2}}$

• s denotes displacement
• u denotes initial velocity
• t denotes time
• a denotes acceleration

⇒ s = ut + (1/2)at²

⇒ s = (5×10) + (1/2)×2×10²

⇒ s = 50 + (1/2)×200

⇒ s = 50 + 100

⇒ s = 150m

Answer 2

▪ Given -

• Initial Velocity (u) = 5m/s
• Acceleration = 2m/s^2
• Time = 10s

▪ To Find -

• Displacement occured in those 10sec

▪ Solution -

To find value of (a), we know second Eqn of Motion,

$★ \: s = </strong><strong>ut</strong><strong> + \frac{1}{2} \: {at}^{2}$

Here,

• S = Displacement
• U = Initial Velocity
• T = time
• A = acceleration

Placing Values,

$⟹s = (5 \times 10) + 2 \times {(10)}^{2}$

$⟹s = 50 + \frac{1}{2} \times 200$

$⟹s = 50 + 100</strong><strong>.</strong><strong>.</strong><strong> </strong><strong>(</strong><strong>Dividing</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>1</strong><strong>/</strong><strong>2</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>by</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>2</strong><strong>0</strong><strong>0</strong><strong>)</strong><strong>$

$⟹s = 150m$

⛬ Motorcyclist displacement is 150m