Answer:
Time taken to accelerate to 48 m/s = 8 seconds
Explanation:
Initially the object is moving south at = [tex]16 m/s[/tex]
So, initial velocity of the object = [tex]16 m/s[/tex]
Acceleration caused by the force = 4 [tex]m/s^2[/tex]
Final velocity towards south = [tex]48 m/s[/tex]
Using equation of motions:
[tex]v_f=v_i+at[/tex]
where
[tex]v_f\rightarrow[/tex] final velocity
[tex]v_i\rightarrow[/tex] initial velocity
[tex]a\rightarrow[/tex] acceleration
[tex]t\rightarrow[/tex] time
Plugging in values.
[tex]48=16+(4)t[/tex]
[tex]48=16+4t[/tex]
Subtracting both sides by 16
[tex]48-16=16+4t-16[/tex]
[tex]32=4t[/tex]
Dividing both side by 4.
[tex]\frac{32}{4}=\frac{4t}{4}[/tex]
[tex]8=t[/tex]
∴ [tex]t=8[/tex]
Time taken to accelerate to 48 m/s = 8 seconds
