A car starts from rest and accelerates at 5m/s2. At t=4s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t=6s?

By Ishita Gupta|Updated : May 24th, 2023

A car starts from rest and accelerates at 5m/s2. At t=4s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t=6s?

Velocity is the rate at which an object changes its position in a specific direction. Whereas Acceleration is the rate at which an object's velocity changes over time. It measures how quickly an object's speed or direction of motion is changing. The velocity and acceleration of the ball at t=6s is 10 m/s².

Velocity Of Ball

Velocity is a vector quantity that describes the rate of change of an object's position in a particular direction. It includes both the speed of an object and the direction in which it is moving. Velocity is calculated by dividing the change in position (displacement) by the change in time. The formula for velocity is:

Velocity = Displacement / Time

Velocity can be positive or negative depending on the direction of motion. Positive velocity indicates motion in one direction, while negative velocity indicates motion in the opposite direction.

Acceleration Of Ball

Acceleration is a vector quantity that measures the rate at which an object's velocity changes over time. It represents how quickly an object's speed or direction of motion is changing. Acceleration can occur when an object speeds up, slows down, or changes direction. Acceleration is calculated by dividing the change in velocity by the change in time. The formula for acceleration is:

Acceleration = Change in Velocity / Time

Acceleration can be positive or negative, depending on the direction of the change in velocity. Positive acceleration indicates an increase in velocity, while negative acceleration (also known as deceleration or retardation) represents a decrease in velocity.

Solution

We need to analyze the motion of the ball and the car separately.

First, let's calculate the velocity and acceleration of the car at t=6s.

The car starts from rest and accelerates at a rate of 5 m/s².

We can use the following equations of motion:

v = u + at

where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

For the car:

Initial velocity (u) = 0 m/s (starting from rest)

Acceleration (a) = 5 m/s²

Time (t) = 6 s

Using the equation, we can find the velocity of the car at t=6s:

v = 0 + 5 * 6

v = 30 m/s

Therefore, the velocity of the car at t=6s is 30 m/s.

Since the car and the ball are in the same frame of reference, the velocity of the ball when dropped will be the same as the velocity of the car at any given time.

Next, let's calculate the acceleration of the ball at t=6s.

The ball is in free fall under the influence of gravity, and its acceleration is constant at approximately 9.8 m/s² (neglecting air resistance).

Therefore, the acceleration of the ball at t=6s will be approximately 9.8 m/s².

Velocity of the ball at t=6s is 30 m/s (the same as the velocity of the car at t=6s).

Acceleration of the ball at t=6s is approximately 10 m/s² (due to gravity).

Summary

A car starts from rest and accelerates at 5m/s2. At t=4s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t=6s?

A car starts from rest and accelerates at 5m/s2. At t=4s, a ball is dropped out of a window by a person sitting in the car. The velocity and acceleration of the ball at t=6s is 10 m/s².

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