Question

Study the given graph and answer the following questions from it :<br />(1) Which part of the graph shows accelerated motion? Calculate the acceleration .<br />(2) Which part of the graph shows retarded motion ?Calculate the retardation .<br />(3) Calculate the distance travelled by the body in first 4 seconds of the journey graphically.

Answer 1

Study the given graph and answer the following questions from it :<br />(1) Which part of the graph shows accelerated motion? Calculate the acceleration .<br />(2) Which part of the graph shows retarded motion ?Calculate the retardation .<br />(3) Calculate the distance travelled by the body in first 4 seconds of the journey graphically.

v = u + at

at t = 0 Velocity = 0 m/s as per graph

u = 0

at t = 4 sec Velocity = 4m/s

4 = 0 + a4

=> a = 1 m/s

0- 4 sec there is acceleration  of 1 m/s

Distance covered in 1st 4 sec

S = ut + (1/2)at²

S = 0 + (1/2)1(4)²

S = 8 m

or we can use

V² - u² = 2aS

=> 4² - 0² = 2×1×S

=> 2S = 16

=> S = 8 m

Distance Covered in 1st 4 sec = 8 m

Distance in 1st 4 sec from graph =

Area covered under graph in 1st 4sec

we can see a right angle triangle with base & Height = 4s & 4m/s respectively

Area = (1/2) base * Height = (1/2) * 4s * 4 m/s = 8 m

at t = 10 Velocity = 4m/s

at t = 14 Velocity = 0 m/s

V = u + at

0 = 4 + a(14-10)

0 = 4 + 4a

=> a = -1 m/s

-ve acceleration is retardation

so 10 to 14 sec there is retardation of 1m/s