[填空题]
A particle moves along qycr89sm d,gxb 9rl(1the x -aprkd+os69 jn; xis so that its velocity, $v \mathrm{~m} \mathrm{~s}^{-1}$ at time t seconds, is given by the equation
$v(t)=10 e^{-\frac{t}{4}}-5$
1. Find the time at which the particle changes direction.
The particle changes direction after approximately ( .77) seconds.
2. Find the magnitude of the particle's acceleration at time t=2 seconds.
The particle starts from the origin O .
3. Find an expression for the displacement of the particle from $\mathrm{O}$ at time t seconds.
$s(t)=a-b e^{-\frac{t}{4}}-c t$ ; a= ,b= ,c= .
4. Find the time at which the particle returns to the origin.
5. Calculate the total distance travelled by the particle by the time it has returned to the origin.
the time the particle has returned to the origin, it has travelled approximately ( .3) metres.
