Question

1.) A car starting from rest is travelling with a constant acceleration of 30 m/s2. Find its velocity after 5 seconds. Find its position after 5 seconds. Find the time it would reach 600 m/s Find the distance it has traveled upon reaching a speed of 600 m/s 2.) A particle travels from 100 m/s to 1000 m/s. Find its constant acceleration if this was done in 5 seconds. What is the distance traveled during the 5 seconds interval? Find the distance travelled if it is travelling with a constant acceleration of 20 m/s2 Find the acceleration of the body is the distance covered during this interval is 1000 meters.

Answer 1

1.)

Initial velocity, $u=0m/s$

Acceleration, $a=30m/s^{2}$

a. Velocity after 5s

Use formula $v=u+at$

$v=0m/s+30m/s^{2}*5s$

ANSWER: ${\color{Red} v=150m/s}$

---------------------------------------

b. Position after 5s

Use formula $s=ut+\frac{1}{2}at^{2}$

$s=0m/s*5s+0.5*30m/s^{2}*(5s)^{2}$

$s=0*5+0.5*30*5^{2}$

ANSWER: ${\color{Red} s=375m}$

---------------------------------------

c. Time to reach 600m/s

Use formula $v=u+at$

$600m/s=0m/s+30m/s^{2}*t$

$600=0+30*t$

$\frac{600}{30}=t$

ANSWER: ${\color{Red} t=20s}$

---------------------------------------

d. Distance traveled to reach 600m/s

Use formula $v^{2}-u^{2}=2as$

$(600m/s)^{2}-(0m/s)^{2}=2*30m/s^{2}*s$

$600^{2}-0^{2}=2*30*s$

$600^{2}=2*30*s$

$\frac{600^{2}}{2*30}=s$

ANSWER: ${\color{Red} s=6000m}$

=================================================

2.)

Initial velocity, $u=100m/s$

Final velocity, $v=1000m/s$

a. Find acceleration if time is 5s

Use formula $v=u+at$

$1000m/s=100m/s+a*5s$

$1000=100+a*5$

$\frac{1000-100}{5}=a$

ANSWER: ${\color{Red} a=180m/s^{2}}$

---------------------------------------

b. Distance traveled in 5s

Use formula $s=ut+\frac{1}{2}at^{2}$

$s=100m/s*5s+0.5*180m/s^{2}*(5s)^{2}$

$s=100*5+0.5*180*5^{2}$

ANSWER: ${\color{Red} s=2750m}$

---------------------------------------

c. Distance traveled if acceleration is 20m/s²

Use formula $v^{2}-u^{2}=2as$

$(1000m/s)^{2}-(100m/s)^{2}=2*20m/s^{2}*s$

$1000^{2}-100^{2}=2*20*s$

$\frac{1000^{2}-100^{2}}{2*20}=s$

ANSWER: ${\color{Red} s=24750m}$

------------------------------------------

d. Find acceleration if the distance traveled is 1000m

Use formula $v^{2}-u^{2}=2as$

$(1000m/s)^{2}-(100m/s)^{2}=2*a*1000m$

$1000^{2}-100^{2}=2*a*1000$

$\frac{1000^{2}-100^{2}}{2*1000}=a$

ANSWER: ${\color{Red} a=495m/s^{2}}$

==================================