Answer :
Answer:
acceleration = 24.23 ms⁻¹
Explanation:
Let's gather the data:
The acceleration of the car is given by a = 0.5 [tex]e^{t}[/tex]
The acceleration is the change in the speed in relation to time. In other words:
[tex]\frac{dv}{dt}[/tex] = a = a = 0.5 [tex]e^{t}[/tex] ...1
Solving the differential equation yields:
v = 0.5 [tex]e^{t}[/tex] + C₁
Initial conditions : 0 = 0.5 [tex]e^{0}[/tex] + C₁
C₁ = -5
at any time t, the velocity is: v= 0.5[tex]e^{t}[/tex]- 5
Solving for distance, s = 0. 5[tex]e^{t}[/tex] - 0.5 t - 0.5
18 = 0.5 [tex]e^{t}[/tex] - 0.5 t - 0.5
t = 3.71 s
Substitute t = 3.71 s
v= 0.5[tex]e^{t}[/tex]- 5
= 19.85 m/s
a = 0.5 [tex]e^{t}[/tex] ...1
= 20.3531
an = [tex]\frac{v^{2} }{p}[/tex]
= [tex]\frac{(19.853)^{2} }{30}[/tex]
= 13.1382
Magnitude of acceleration = [tex]\sqrt{ (a)^{2} + (an)^{2} }[/tex]
= [tex]\sqrt{(20.3531)^{2} +(13.1382)^{2} }[/tex]
= 24.23 ms⁻¹ Ans