Figure given above shows the velocity-time graphs for two cars A and B moving in the same direction. Which car has greater acceleratio? Give reason to your answer
Answers
Answer:
Car B has more acceleration than car A
Explanation:
Acceleration is defined as the rate of change of velocity per unit time
Mathematically it is represented as,
Acceleration = Change in Velocity / Time taken
a = Δv / Δt
For any given graph to find the slope we take,
Slope = Change in y-coordinate / Change in x-coordinate
Slope = (y₂ - y₁) / (x₂ - x₁)
Hence for a Velocity - Time Graph,
Slope = (y₂ - y₁) / (x₂ - x₁)
Slope = Change in velocity / Change in time
Change in time implies the time taken
Hence,
Slope = Change in velocity / Time taken
Slope = Acceleration
Hence,
Slope of Velocity - Time graph gives acceleration
We also know that,
Slope = tanθ
Hence,
if θ increases, value of tanθ also increases
if tanθ increases, value of slope increases
Therefore,
the car having a larger angle with the X-axis (larger θ) will have more slope which in turn implies as the acceleration
Since, slope of car B is greater than slope of car A
acceleration of car B is greater than slope of car A
Answer:
since the slope of VT graph for car b is greater than that of car a the acceleration of the car we would be greater than that of car A