ABSTRACT:To analyze the motion of a family car as projected in the v-t graph and then approximate the a-t,

s-t graphs out of it. This can be the most common driving experience just plotted for a short time span.

ANALYSIS: Vdv=ads

dsdt

=v

dvdt

=a

But here we are not given any relation between motion parameters so we will use the slope determination technique to find the acceleration of the car, since slope of v-t graph is acceleration.

1. Here the motion represents straight line for 0-40 sec of velocity i.e., 0 acceleration.2. For 40-80 sec of velocity we have acceleration of:

v 2−v1t 2−t 1 =>

0−1080−40=>-0.25=>

m

s2

0-40 sec interval: Velocity is constant at 10 m/s

dsdt

=v =>vdt=ds =>v∗∫¿

t

dt=∫so

s

ds =>v*(t-t0) =s-s0 @s0=0 , t0=0

The case of “0” acceleration, s=v*t. v*(t) =s , =>s=0.25*40 ,=>s=10m the car is just moving with constant velocity for 40 sec and equal distance of 10 meters is

covered every second.

0-80 sec interval:

Acceleration is constant = -0.25 m

s2

Vf=Vi+at, Vf=10-0.25*40, =>Vf=0

Vf=Vi-0.25*(t80-t40)

S=Vt*(t-t40)-0.125*(t-t40)2

S80=0*40-0.125*402=-200=200 m

in this formula when we will be calculating the distance just for a first sight it will seems to give first +ve increasing distance and then –ve distance , this is actually due to the made of this formula which is based on the distance covered in the verge of velocity Vt at that time t (Vi*t), and distance covered in the verge of acceleration or deceleration ,but if in case of deceleration distance is –ve we take its mode (distance cannot be -ve),and adding them up in that case.

o So then the distance should come positive and increasing in concerned direction of motion and for a variable motion scenario previous distance covered is to be added for actual distance covered evaluation(in this final case distances direction can be taken into account).

0 10 20 30 40 50 60 70 80 900

100200300400500600700

s-t

Series2

time sec

dist

ance

met

ers

0 10 20 30 40 50 60 70 80 900

0.05

0.1

0.15

0.2

0.25

0.3

a-t

Series2

time sec

acce

lera

tionm

/s^2

ANNEXURE:TABLE 1:

t s a v0 0 0 101 10 0 102 20 0 103 30 0 104 40 0 105 50 0 106 60 0 107 70 0 108 80 0 109 90 0 10

10 100 0 1011 110 0 1012 120 0 1013 130 0 1014 140 0 1015 150 0 1016 160 0 1017 170 0 1018 180 0 1019 190 0 1020 200 0 1021 210 0 1022 220 0 1023 230 0 1024 240 0 10

25 250 0 1026 260 0 1027 270 0 1028 280 0 1029 290 0 1030 300 0 1031 310 0 1032 320 0 1033 330 0 1034 340 0 1035 350 0 1036 360 0 1037 370 0 1038 380 0 1039 390 0 1040 400 0 1041 409.875 0.25 9.7542 419.5 0.25 9.543 428.875 0.25 9.2544 438 0.25 945 446.875 0.25 8.7546 455.5 0.25 8.547 463.875 0.25 8.2548 472 0.25 849 479.875 0.25 7.7550 487.5 0.25 7.551 494.875 0.25 7.2552 502 0.25 753 508.875 0.25 6.7554 515.5 0.25 6.555 521.875 0.25 6.2556 528 0.25 657 533.875 0.25 5.7558 539.5 0.25 5.559 544.875 0.25 5.2560 550 0.25 561 554.875 0.25 4.7562 559.5 0.25 4.563 563.875 0.25 4.2564 568 0.25 465 571.875 0.25 3.7566 575.5 0.25 3.567 578.875 0.25 3.25

68 582 0.25 369 584.875 0.25 2.7570 587.5 0.25 2.571 589.875 0.25 2.2572 592 0.25 273 593.875 0.25 1.7574 595.5 0.25 1.575 596.875 0.25 1.2576 598 0.25 177 598.875 0.25 0.7578 599.5 0.25 0.579 599.875 0.25 0.2580 600 0.25 0