Motion In A Straight Line

We are given the following statements, and we need to identify which one is incorrect:

• The state of rest or uniform linear motion both imply zero acceleration: This is correct. According to Newton's first law of motion, when a body is at rest or moving with uniform velocity, it has zero acceleration.
• A net force is needed to keep a body in uniform motion: This is incorrect. In the case of uniform motion (in a straight line), no net force is required to keep the body moving. According to Newton's first law, an object in motion will stay in motion with constant velocity unless acted upon by an external force.
• Inertia means resistance to change: This is correct. Inertia refers to an object's tendency to resist changes in its state of motion (either rest or uniform motion).
• The rate of change of momentum is proportional to the applied force: This is correct. According to Newton's second law, the rate of change of momentum is directly proportional to the applied force.
• Momentum is a vector quantity: This is correct. Momentum is a vector quantity because it has both magnitude and direction, which are dependent on the velocity of the object.

Correct Answer:

Correct Answer: (E) A net force is needed to keep a body in uniform motion

We can use the kinematic equation to find the acceleration: Where: - is the distance covered (120 m), - is the initial velocity (0 m/s, since the cyclist starts from rest), - is the acceleration, - is the time taken (10 s). Substituting the known values into the equation: Simplifying:

The correct option is (C) :

Given:

• Particle starts from rest at the origin.
• Constant acceleration makes a angle with the positive y-axis.
• Displacement along y-axis is 10 m in 2 seconds.

Step 1: Resolve Acceleration into Components

The acceleration can be resolved into:

Step 2: Apply Kinematic Equation for y-Displacement

Since the particle starts from rest, its initial velocity . The displacement along the y-axis is given by:

Substitute , , and :

Conclusion:

The magnitude of the acceleration is 10 ms .

Answer:

The average speed of an object is defined as the total distance traveled divided by the total time taken. In this case, the car travels a distance of 10 m. We need to find the time it takes for the car to come to rest.

We can use the following equations of motion:

1. 2. 3.

Here, m/s (initial speed), m/s (final speed), m (distance), and we need to find (time).

We can use equation (3) to find the acceleration: m/s

Now we can use equation (1) to find the time: s

Now we can calculate the average speed: Average speed m/s.

Final Answer: The final answer is

A displacement-time graph with a straight-line pattern implies that the rate of change of displacement remains constant,
meaning: Since velocity is uniform, acceleration must be zero, ruling out options involving acceleration.