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__SPEED, VELOCITY AND ACCELERATION__

**Speed:**Distance travelled by an object per unit time is called speed.

**speed= distance travelled / time take**

- Speed has only magnitude and no direction,so it is scalar quantity.

**Average speed = total distance travelled / total time taken**

**Instantaneous speed**:The speed of an object at any particular instant of time is called the instantaneous speed.

**V**

_{ins}= dx/dt**Velocity:**The rate of change of position of an object with respect to time in a given direction is called velocity.

**velocity = displacement /time**

- velocity has both magnitude and direction,so it is vector quantity.

**Average velocity = total displacement/total time**

**V**

_{av}=∆x/∆t**Instantaneous velocity:**The velocity of an object at a particular instant of time is called instantaneous velocity.

**V**

_{ins}= dx/dt**Acceleration:**The rate of change of velocity of an object with respect to time is called acceleration.

- It has both magnitude and acceleration.so,it is vector quantity.

**Average acceleration = change in velocity/ time taken**

**A**

_{av}=**∆v/∆t**

**Instantaneous acceleration:**The acceleration of an object at a particular instant of time is called instantaneous acceleration.

**a**

_{ins}= dv/dt

**V = dx/dt**

**a**

_{ins}= d^{2}x/dt^{2}###
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__Conceptual questions__

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__Conceptual questions__

**1.Can the speed of a body be negative?**

Ans: NO,because speed is distance travelled by a body per unit time and distance is total path length travelled by a body which is never negative.

Ans: No,velocity is basically speed with direction.If velocity is constant ,it means speed and direction both are constant.

Ans: Yes,as velocity is speed with direction ,if speed is constant but changing direction then velocity will be varying.For ex- In uniform circular motion speed remains constant but due to changing direction, velocity keeps changing at every point.

Ans: Yes, when a body is thrown vertically upwards,at the highest point its velocity becomes zero but has acceleration due to gravity.

Ans: Yes.when an object is thrown vertically upwards,the direction of velocity changes during its rise and fall while acceleration acts always downwards and remains constant.

Ans: When a body is moving with constant velocity i.e. In Uniform Motion.

Ans: Not necessarily.If velocity increases,acceleration acts in the direction of velocity and if velocity decreases ,acceleration acts in the direction opposite to direction of velocity.

Ans: Both the balls will rise to the same heights,because distance covered by a body does not depend on the mass for a given initial speed and acceleration.

Ans: During motion under gravity,a body returns back to the point of projection with the speed equal to the speed with which it is thrown up.so, both the balls will acquire same speed.

Ans: No.As acceleration is rate of change of velocity,zero acceleration means there is no change in velocity but constant acceleration means velocity increases or decreases with constant rate.

**2. Can a body have a constant velocity and still have a varying speed?**Ans: No,velocity is basically speed with direction.If velocity is constant ,it means speed and direction both are constant.

**3. Can a body have a constant speed and still have a varying velocity?**Ans: Yes,as velocity is speed with direction ,if speed is constant but changing direction then velocity will be varying.For ex- In uniform circular motion speed remains constant but due to changing direction, velocity keeps changing at every point.

**4. Can a body has zero velocity and still has acceleration?**Ans: Yes, when a body is thrown vertically upwards,at the highest point its velocity becomes zero but has acceleration due to gravity.

**5. Can the direction of velocity of an object change ,when acceleration is constant?**Ans: Yes.when an object is thrown vertically upwards,the direction of velocity changes during its rise and fall while acceleration acts always downwards and remains constant.

**6. Under what condition is the average velocity equal to its instantaneous velocity?**Ans: When a body is moving with constant velocity i.e. In Uniform Motion.

**7. Is the direction of acceleration same as direction of velocity?**Ans: Not necessarily.If velocity increases,acceleration acts in the direction of velocity and if velocity decreases ,acceleration acts in the direction opposite to direction of velocity.

**8. Two balls of different masses are thrown vertically upward with same initial speed.Which one will rise to greater height?**Ans: Both the balls will rise to the same heights,because distance covered by a body does not depend on the mass for a given initial speed and acceleration.

**9. Two balls of different masses are thrown vertically upwards with the same speed.Which one will pass through the point of projection in their downward direction with greater speed?**Ans: During motion under gravity,a body returns back to the point of projection with the speed equal to the speed with which it is thrown up.so, both the balls will acquire same speed.

**10. Are constant acceleration and zero acceleration the same?**Ans: No.As acceleration is rate of change of velocity,zero acceleration means there is no change in velocity but constant acceleration means velocity increases or decreases with constant rate.

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