Answer:
a) 27.3 m/s
b) 3.78 s
c) 10.576 s
Explanation:
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration
a)
[tex]v=u+at\\\Rightarrow v=0+4.2\times 6.5\\\Rightarrow v=27.3\ m/s[/tex]
Top speed of the gazelle is 27.3 m/s
b)
[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow 30=0t+\frac{1}{2}\times 4.2\times t^2\\\Rightarrow t=\sqrt{\frac{30\times 2}{4.2}}\\\Rightarrow t=3.78\ s[/tex]
The gazelle would take 3.78 seconds to win a 30 m race.
c)
[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow s=0\times 6.5+\frac{1}{2}\times 4.2\times 6.5^2\\\Rightarrow s=88.725\ m[/tex]
The gazelle would go 88.725 m with the acceleration after which there will be no acceleration.
Time = Distance / Speed
[tex]\text{Time}=\frac{200-88.725}{27.3}=4.076\ s[/tex]
Total time taken by the gazelle to cover 200 m would be 6.5+4.076 = 10.576 seconds
