Physics Past Paper PDF - Equations of Motion

Activity _____________ 7.10 Feroz and his sister Sania go to school on their bicycles. Both of them start at the same time from their home but take different times to reach the school although they follow the same route. Table 7.5 shows the distance travelled by them in different times Table 7.5: Di...

Activity _____________ 7.10 Feroz and his sister Sania go to school on their bicycles. Both of them start at the same time from their home but take different times to reach the school although they follow the same route. Table 7.5 shows the distance travelled by them in different times Table 7.5: Distance covered by Feroz and Sania at different times on their bicycles Time Distance travelled by Feroz (km) Distance travelled by Sania (km) 8:00 am 0 0 8:05 am 1.0 0.8 8:10 am 1.9 1.6 8:15 am 2.8 2.3 8:20 am 3.6 3.0 8:25 am – 3.6 Q Plot the distance-time graph for their motions on the same scale and interpret. uestions 4. What is the quantity which is measured by the area occupied below the velocity-time graph? 7.5 Equations of Motion When an object moves along a straight line with uniform acceleration, it is possible to relate its velocity, acceleration during motion and the distance covered by it in a certain time interval by a set of equations known as the equations of motion. For convenience, a set of three such equations are given below: v = u + at (7.5) s = ut + ½ at2 (7.6) 2 a s = v2 – u2 (7.7) where u is the initial velocity of the object which moves with uniform acceleration a for time t, v is the final velocity, and s is the distance travelled by the object in time t. Eq. (7.5) describes the velocity-time relation and Eq. (7.6) represents the position-time relation. Eq. (7.7), which represents the relation between the position and the velocity, can be obtained from Eqs. (7.5) and (7.6) by eliminating t. These three equations can be derived by graphical method. Example 7.5 A train starting from rest attains a velocity of 72 km h –1 in 5 minutes. Assuming that the acceleration is uniform, find (i) the acceleration and (ii) the distance travelled by the train for attaining this velocity. Solution: 1. What is the nature of the distance-time graphs for uniform and non-uniform motion of an object? 2. What can you say about the motion of an object whose distance-time graph is a straight line parallel to the time axis? 3. What can you say about the motion of an object if its speedtime graph is a straight line parallel to the time axis? We have been given u = 0 ; v = 72 km h–1 = 20 m s-1 and t = 5 minutes = 300 s. (i) From Eq. (7.5) we know that a= (v – u ) t = 20 m s –1 – 0 m s –1 300 s = 1 m s –2 15 81 MOTION Rationalised 2023-24