8.3- Motion along a straight line at constant acceleration

Question 1

State what each word stands for, with their desired units

S

U

V

A

T

Answer 1

S = displacment (m)

U = inital velocity (ms^-1)

V = final velocity (ms^-1)

A = acclertaion (ms^-2)

T = time (s)

Question 2

state the 5 main SUVAT equations

Answer 2

v = u + at

S = 0.5(v+u)t

s = ut + 0.5at² OR s = vt - 0.5at²

v² = u² + 2as

Question 3

Prove v = u + at

Answer 3

since a = (v-u) / t (on graphs)

reagranges; v = u + at

Question 4

Prove s = 0.5(v+u)t

Answer 4

since; s = average speed x t

average speed; 0.5(v+u)

thus; s = 0.5(v+u)t

Question 5

Prove s = ut + 0.at²

Answer 5

since; s = average speed x t

average speed; 0.5(v+u)

thus; s = 0.5(v+u)t

and; v = u + at, to elimate v

s = 0.5(u + (u+at))t = 0.5 (2u + at)t = 0.5 (2ut + at²) = ut + 0.5at²

Question 6

Prove v² = u² + 2as

Answer 6

combine; a = (v-u)/t & s = 0.5(u+v)t

as = [(v-u)/t] x [0.5(u+v)t]

as = 0.5(v-u)(v+u) = 0.5(v²-u²)

reranges; v² = u² + 2as

Question 7

velocity - time graphs

1- what does the gradient =

2- what does the area under the graphs =

Answer 7

1- acceleration

2 - displacement