Question

The velocity of a particle is given by v = 217 - 116t+ 33, where v is in meters per second and t is in seconds. Plot the velocity v and acceleration a versus time for the first 6.7 seconds of motion and evaluate the velocity when a is zero. Make the plots and then answe the questions. Questions: When t = 0.7 s, ya m/s2 When t = 3.4 5, y = Im/s, a - Im/s, a - m/s, a - m/s2 When t - 4.7 sve m/s² When a = 0, y = m/s Click if you would like to Show Work for this question: Modify Show Work

Answer 1

Since, we know,

a=dv/dt

Therefore, for corresponding values of t and v, we first plot the Velocity-time graph which is parabolic.

After that, using a=dv/dt we find corresponding values of a and t, which give us a-t graph which is linear.

VT graph

V=214²-110t+33 a = dv = dialt²_110t +33) dt عام z 42€ -110

14.7,-20.1099999999909) (0.7,-33.71000000000001) -100- 13.4,-98.24000000000004) 6 2 3 5

A-t graph

14.7,87.4) 13.4,32.79999999999998) 10.7,-80.6) -100

For respective values, we match values from graph or manually calculate using equations

a) at t=0.75, Vz 2110.7)2-11010.7)+ 33 - - 33.71 mis Q = 4210.7)-110 = -80.6m/s? B) at t= 3.4s, Vedli (3.42-11013.4)+33= -98-24 mis a = 42(3.4)-110 = 32.79 m/s2 -c) at t = 4,75 Va 21(467)2 - 110(4.7) + 38 = -20.11 m/s a- 4214.7)-110 = 87.4m/s2

For v at a=0,

d) fou a o, 42Lt) -110 =0 =) t = 2.625 o oo v at t=20625, V=211262)2 = 1101262)+33 3 11.047 mis.