The velocity of the car after 10 s is 78.95 km/hr
Explanation:
Given:
m = 1,250 kg
[tex]v_i[/tex] = 30 km/hr
F = 1,700 N
t = 10 s
Required:
Final velocity
Equation:
Force
F = ma
where: F - force
m - mass
a - acceleration
Acceleration
a = [tex]\frac{v_f \:-\:v_i}{t}[/tex]
where: a - acceleration
[tex]v_i[/tex] - initial velocity
[tex]v_f[/tex] - final velocity
t - time elapsed
Solution:
Solve for acceleration using the formula for force
F = ma
Substitute the value of F and m
(1700 N) = (1250 kg)(a)
a = [tex]\frac{1700\:N}{1250\:N}[/tex]
a = 1.36 m/s²
Solve for final velocity using the formula for acceleration
= [tex]\frac{30\:km}{hr}\:×\:\frac{1000\:m}{1\:m}\:×\:\frac{1\:hr}{3600\:s}[/tex]
= [tex] 8.33 m/s [/tex]
- Substitute the value of a, [tex]v_i[/tex] and t
a = [tex]\frac{v_f \:-\:v_i}{t}[/tex]
[tex]1.36\: m/s² \:= \:\frac{v_f \:-\:8.33\:m/s}{10\:s}[/tex]
[tex](10 \:s)1.36\: m/s² \:= \:v_f \:-\:8.33\:m/s[/tex]
[tex]v_f\: =\: (10 \:s)1.36 \:m/s²\: + \:8.33\:m/s[/tex]
[tex]v_f \: =\: 13.6 \:m/s \:+\: 8.33\:m/s[/tex]
[tex]v_f\: =\: 21.93\: m/s[/tex]
= [tex]\frac{21.93\:m}{s}\:×\:\frac{1\:km}{1000\:m}\:×\:\frac{3600\:s}{1/:hr}[/tex]
= [tex]78.95\: km/hr[/tex]
Final answer
The velocity of the car after 10 s is 78.95 km/hr
