A car initially at rest starts moving with a constant acceleration of 0.5 m / s ^ 2 and travels a distance of 49m . Find its final velocity and the time taken .
Answers
Required Answer:
• The final velocity of the car = 5 m/s • The time taken by the car = 10 seconds
Given :
• Initial velocity of the car = 0 m/s
• Acceleration of the car = 0.5 m/s² • Total distance travelled by the car = 25 m
To find :
• Final velocity of the car • Time taken by the car
Solution :
To calculate the final velocity of the car, we will use the third equation of motion.
Third equation of motion :
v² - u² = 2as
where,
• v denotes the final velocity
• u denotes the initial velocity
• a denotes the acceleration • s denotes the distance travelled/displacement
Substituting the given values:
→ v² - (0)² = 2(0.5)(25)
→ v² -0 = 2 × 5/10 × 25
→ v² = 5/5 x 25
v² = 25
→ Taking square root on both the sides :
⇒ V = √25
→ V = √(5 × 5)
⇒ V = 5
Therefore, the final velocity of the car = 5 m/s
To calculate the time taken by the car, we will use the first equation of motion.
First equation of motion :
• Vu+ at
where,
• v denotes the final velocity
u denotes the initial velocity
• a denotes the acceleration • t denotes the time taken
Substituting the given values:
5 = 0 + 0.5 x t
→ 50.5 xt
→ 5/0.5 = t
→ 5 × 10/5
⇒ 10 = t
Therefore, the time taken by the car = 10 seconds